Apollonius <Pergaeus>, Apollonii Pergaei Conicorvm Lib. V. VI. VII. paraphraste Abalphato Asphahanensi : nunc primum editi ; additvs in calce Archimedis assvmptorvm liber, ex codibvs arabicis mss Abrahamus Ecchellensis Maronita latinos reddidit, Jo. Alfonsvs Borellvs curam in geometricis versione contulit & [et] notas vberiores in vniuersum opus adiecit

Page concordance

< >
Scan Original
111 73
112 74
113 75
114 76
115 77
116 78
117 79
118 80
119 81
120 82
121 83
122 84
123 85
124 86
125 87
126 88
127 89
128 90
129 91
130 92
131 93
132 94
133 95
134 96
135 97
136 98
137 99
138 100
139 101
140 102
< >
page |< < (247) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div783" type="section" level="1" n="242">
          <p style="it">
            <s xml:id="echoid-s9248" xml:space="preserve">
              <pb o="247" file="0285" n="285" rhead="Conicor. Lib. VI."/>
            I S, vt F K ad K L: </s>
            <s xml:id="echoid-s9249" xml:space="preserve">ſed erat D B ad B E, vt F I ad I S; </s>
            <s xml:id="echoid-s9250" xml:space="preserve">igitur F K ad K L
              <lb/>
            eandem proportionem habebit: </s>
            <s xml:id="echoid-s9251" xml:space="preserve">quàm D B ad D E.</s>
            <s xml:id="echoid-s9252" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9253" xml:space="preserve">Et educamus in triangulo chordam M N parallelam K F, & </s>
            <s xml:id="echoid-s9254" xml:space="preserve">æqualem
              <lb/>
              <note position="left" xlink:label="note-0285-01" xlink:href="note-0285-01a" xml:space="preserve">b</note>
            D B, &</s>
            <s xml:id="echoid-s9255" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9256" xml:space="preserve">Non vna, ſed duplex recta linea M N duci poteſt parallela cuilibet
              <lb/>
            duarum F K, quæ interius ſubtendat angulum verticis F trianguli H F I per
              <lb/>
            axim ducti. </s>
            <s xml:id="echoid-s9257" xml:space="preserve">Et poteſt etiam effici M N æqualis ipſi D B, vt in expoſitione præ-
              <lb/>
            cedentis propoſitionis oſtenſum eſt.</s>
            <s xml:id="echoid-s9258" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9259" xml:space="preserve">Itaque planum, tranſiens per M N, producit in cono H F I ſectionem
              <lb/>
              <note position="left" xlink:label="note-0285-02" xlink:href="note-0285-02a" xml:space="preserve">c</note>
            ellipticam æqualem ſectioni A B; </s>
            <s xml:id="echoid-s9260" xml:space="preserve">quia, &</s>
            <s xml:id="echoid-s9261" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9262" xml:space="preserve">Addidi verba, quæ in textu
              <lb/>
            deſiderantur, vt ſenſus perfectus ſit.</s>
            <s xml:id="echoid-s9263" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9264" xml:space="preserve">Ergo duæ illæ ſectiones ſunt æquales, &</s>
            <s xml:id="echoid-s9265" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9266" xml:space="preserve">Concipi debet ſectio N O M
              <lb/>
              <note position="left" xlink:label="note-0285-03" xlink:href="note-0285-03a" xml:space="preserve">d</note>
            P, duplex, quia nimirum duæ ſectiones ſub contrariæ, æquales ſunt, vt faci-
              <lb/>
            le cum Mydorgìo oſtendi poteſt.</s>
            <s xml:id="echoid-s9267" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9268" xml:space="preserve">Et dico, quod non reperiatur in cono H F I ſectio elliptica, habens
              <lb/>
              <note position="left" xlink:label="note-0285-04" xlink:href="note-0285-04a" xml:space="preserve">e</note>
            verticem ſuper F I; </s>
            <s xml:id="echoid-s9269" xml:space="preserve">quia ſi poſſibile eſſet, &</s>
            <s xml:id="echoid-s9270" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9271" xml:space="preserve">Textus valde corruptus ex-
              <lb/>
            poſito modo reſtitui debere conſtat ex progreſſu demonſtrationis.</s>
            <s xml:id="echoid-s9272" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9273" xml:space="preserve">Et diuidendo F R maior ad minorem R Q eſt vt F L minor ad maio-
              <lb/>
              <note position="left" xlink:label="note-0285-05" xlink:href="note-0285-05a" xml:space="preserve">f</note>
            rem K L, &</s>
            <s xml:id="echoid-s9274" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9275" xml:space="preserve">Supplendæ fuerunt particulæ aliquæ ad tollendam equiuocatio-
              <lb/>
            nem.</s>
            <s xml:id="echoid-s9276" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div790" type="section" level="1" n="243">
          <head xml:id="echoid-head304" xml:space="preserve">SECTIO VNDECIMA</head>
          <head xml:id="echoid-head305" xml:space="preserve">Continens Propoſit. XXIX. XXX.
            <lb/>
          & XXXI.</head>
          <head xml:id="echoid-head306" xml:space="preserve">PROPOSTIO XXIX.</head>
          <p>
            <s xml:id="echoid-s9277" xml:space="preserve">DAto cono recto A B C, conum exhibere ei ſimilem, qui
              <lb/>
            datam ſectionem D E F contineat, cuius axis E G, & </s>
            <s xml:id="echoid-s9278" xml:space="preserve">
              <lb/>
            erectus E H; </s>
            <s xml:id="echoid-s9279" xml:space="preserve">ſitque prius ſectio parabole.</s>
            <s xml:id="echoid-s9280" xml:space="preserve"/>
          </p>
          <figure number="333">
            <image file="0285-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0285-01"/>
          </figure>
          <p>
            <s xml:id="echoid-s9281" xml:space="preserve">Super E G educatur planum ad ſectionem D
              <lb/>
            E F ad angulos rectos eleuatum, in quo duca-
              <lb/>
            tur E I K, quæ contineat cum E G angulum
              <lb/>
            æqualem ipſi angulo C: </s>
            <s xml:id="echoid-s9282" xml:space="preserve">& </s>
            <s xml:id="echoid-s9283" xml:space="preserve">ponamus E H ad E
              <lb/>
              <note position="left" xlink:label="note-0285-06" xlink:href="note-0285-06a" xml:space="preserve">a</note>
            K, vt A C ad C B, & </s>
            <s xml:id="echoid-s9284" xml:space="preserve">faciamus ſuper E K tri-
              <lb/>
            angulum E L K ſimile triangulo A B C, vt an-
              <lb/>
            gulus verticalis L æqualis ſit angulo B. </s>
            <s xml:id="echoid-s9285" xml:space="preserve">Facia-
              <lb/>
            mus etiam conum, cuius vertex ſit L, eiuſque
              <lb/>
            baſis circulus, cuius diameter ſit E K, qui ſit
              <lb/>
            eleuatus ſuper triangulum E L K ad angulos re-
              <lb/>
            ctos: </s>
            <s xml:id="echoid-s9286" xml:space="preserve">erit igitur angulus E K L æqualis ipſi </s>
          </p>
        </div>
      </text>
    </echo>
Impressum